Asymptotic Quasi-likelihood Based on Kernel Smoothing for Multivariate Heteroskedastic Models with Correlation

This paper considers parameter estimation in multivariate heteroscedastic models with unspecific correlation. In this paper, we propose an asymptotic quasi-likelihood (AQL) approach which utilises a nonparametric kernel estimator of variance covariances matrix ∑ to replace the true ∑ in the standard quasi-likelihood. The kernel estimation avoids the risk of potential missspecification of ∑ and thus make the parameter estimator more robust. The well developed theory framework for AQL (See Lin, 2000) provides a solid base for ensuring the efficiency of the approach developed in this paper. This has been further verified by empirical studies carried out in this paper.